Matrix and determinant are two completely different concepts. A determinant represents a number, while a matrix is just an ordered arrangement of some numbers. Using the tool of matrix, the coefficients in linear equations can be formed into vectors in vector space; In this way, a series of theoretical problems such as the solution of a multivariate linear equation system and the relationship between different solutions can be completely solved.
Matrix is an important basic concept in mathematics, the main research object of algebra and an important tool for mathematical research and application. The word "matrix" was first used by Sylvester, who invented this predicate to distinguish rectangular arrays from determinants. In fact, the subject of matrix has developed very well before it was born. It is obvious from a lot of work on determinant that for many purposes, whether the value of determinant is related to the problem or not, the square matrix itself can be studied and utilized, and many basic properties of matrix are also established in the development of determinant. Logically, the concept of matrix should precede the concept of determinant, but in history, the order is just the opposite.
Firstly, matrix was put forward as an independent mathematical concept, and a series of articles on this subject were published first. Gloria combined with the study of invariants under linear transformation, first introduced matrix to simplify notation. From 65438 to 0858, he published the first paper on the subject, Research Report on Matrix Theory, which systematically expounded the theory of matrix. In this paper, he defined a series of basic concepts such as matrix equality, matrix operation rule, matrix transposition and matrix inversion, and pointed out the interchangeability and combinability of matrix addition. In addition, Gloria also gives the characteristic equation and characteristic root (eigenvalue) of the square matrix and some basic results about the matrix. Gloria was born in an old and talented English family. After graduating from Trinity College, Cambridge University, he stayed to teach mathematics. Three years later, he switched to the profession of lawyer, and his work was fruitful. He studied mathematics in his spare time and published a large number of mathematical papers.
In 1855, emmett (C.Hermite, 1822 ~ 190 1) proved the special properties of the characteristic roots of some matrix classes discovered by other mathematicians, such as the characteristic roots of emmett matrices now. Later, Klebsch (A A. Clebsch, 183 1 ~ 1872) and A.Buchheim proved the characteristic root property of symmetric matrices. H.Taber introduced the concept of trace of matrix and gave some related conclusions.
In the history of matrix theory, the contribution of G. Frobenius (1849-1917) is indelible. He discussed the minimum polynomial problem, introduced the concepts of matrix rank, invariant factor and elementary factor, orthogonal matrix, similar transformation of matrix and contraction matrix, arranged the theories of invariant factor and elementary factor in logical form, and discussed some important properties of orthogonal matrix and contraction matrix. In 1854, Jordan studied the problem of transforming a matrix into a standard form. 1892, Metzler introduced the concept of matrix transcendental function and wrote it in the form of matrix power series. In the works of Fourier, Searle and Poincare, the problem of infinite order matrix is also discussed, which is mainly to meet the needs of equation development.
The properties of the matrix itself depend on the properties of the elements. After more than two centuries of development, matrix has become an independent branch of mathematics-matrix theory. Matrix theory can be divided into matrix equation theory, matrix decomposition theory and generalized inverse matrix theory. Matrix is widely used in many aspects, not only in the field of mathematics, but also in the fields of mechanics, physics, science and technology.